Here's the thing; this commenter got it exactly backwards. It's true that "male privilege is being able to not think about gender", but that's BECAUSE THE MALE GENDER IS ASSUMED THE STANDARD. So men don't have to bother themselves to familiarize with women's experiences, and thus don't have to "think about gender". Women, as the "other gender", have to deal with male-centered culture all the damn time, where the male perspective/motivation is presented constantly. Thus women have a better idea of what it's like to be a man than men have of what it's like to be a woman. If it were about lived experiences, the average woman would be a much better "everyman" (eugh, typing that word made my stomach turn a little).
I think the reason for using an “everyman” instead of an “everywoman” is because women, being women, have specific experiences as women. A female character is aware of her gender. An everyman character can have both male and female experiences, and become somewhat androgynous (ie. Nemo).
It’s privilege, I admit. White privilege is being able to not think about race, and male privilege is being able to not think about gender.
But it's not about lived experiences. It's about what the audience can project onto the characters. In this case, this commenter sees women, clearly, as the "special case" gender who can only experience womanly things, whereas men are objective observers. Men are the default, women are the other. AGAIN.
Basically, what this douchenozzle is saying is, "Men are the standard, because men are the standard!! People notice when girls are girls. Because they're girls! Duh. That's what male privilege means!"
OK, so maybe he's unintentionally closer to the truth than I'm giving him credit for...